Revealing mistake: In episode four, when Caber breaks a piece off the Zygon equipment, the entire wall shakes.
Revealing mistake: In episode four, when Vishinsky and Sarah go into the storage room to get the force field generators, the plaque on the door flops around like the cardboard that it is.
Revealing mistake: The "crystal" tube holding Sarah wobbles whenever it is touched.
Revealing mistake: In order to save money filming the lift-off of Crayford's rocket from Oseidon, the producers decided to use stock footage of a Saturn 5 blast-off. Unfortunately, that meant the words "UNITED STATES" in large red lettering are seen on the side of the rocket...which is a little bit of a giveaway, especially as the rocket is supposed to be a BRITISH space probe.
Revealing mistake: When the Morbius creature falls over the cliff, he bumps into the camera.
Revealing mistake: The fake snow in episodes one and two is effective - with the exception of when the Doctor is digging up the second Krynoid pod, where it is painfully obvious the snow is styrofoam packing peanuts.
Answer: TARDISes are generally available for properly authorised use on Gallifrey; they're not usually assigned to a particular Timelord on a long-term basis. The Doctor stole his when he left his homeworld.
Tailkinker ★